The Stacks project

Lemma 26.7.5. Let $(X, \mathcal{O}_ X) = (\mathop{\mathrm{Spec}}(R), \mathcal{O}_{\mathop{\mathrm{Spec}}(R)})$ be an affine scheme. The functors $M \mapsto \widetilde M$ and $\mathcal{F} \mapsto \Gamma (X, \mathcal{F})$ define quasi-inverse equivalences of categories

\[ \xymatrix{ \mathit{QCoh}(\mathcal{O}_ X) \ar@<1ex>[r] & \text{Mod}_ R \ar@<1ex>[l] } \]

between the category of quasi-coherent $\mathcal{O}_ X$-modules and the category of $R$-modules.

Comments (2)

Comment #427 by Jeroen Zuiddam on

I am getting a parse error in the display.

Comment #428 by on

OK, I think this is due to an XyJax parsing error. I'll investigate more. Thanks for the report!

There are also:

  • 5 comment(s) on Section 26.7: Quasi-coherent sheaves on affines

Post a comment

Your email address will not be published. Required fields are marked.

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).

Unfortunately JavaScript is disabled in your browser, so the comment preview function will not work.

All contributions are licensed under the GNU Free Documentation License.

In order to prevent bots from posting comments, we would like you to prove that you are human. You can do this by filling in the name of the current tag in the following input field. As a reminder, this is tag 01IB. Beware of the difference between the letter 'O' and the digit '0'.